I added these two problems together because i thought since i only need help with one part of the random sample 17 i can myself another question help. I can't find the critical value for it. I tried -2.583 and 2.583 and my professor says it still wrong. If this problem can be specified on how to get it exactly with the correct answer it will be gladly appreciatedthe other problem i need help with the 3 empty boxes. please and thank you ### Hypothesis Testing ExampleA random sample of 17 observations taken from a normally distributed population produced a sample mean of 42.4 and a standard deviation of 8. Find the range for the p-value and the critical and observed values of $ t $ for the following test of hypotheses, using $ \alpha = 0.01 $.**Objective:**Use the t-distribution table to find a range for the p-value. Round your answers for the values of $ t $ to three decimal places.**Hypothesis:**- $ H_0: \mu = 46 $- $ H_1: \mu < 46 $**p-value Range:**- $ 0.025 < \text{p-value} < 0.05 $**Critical Value and Observed Value:**- $ t_{\text{critical}}: $ (Value to be determined using a t-distribution table)- Observed $ t $ value: $ t_{\text{observed}} = -1.856 $**Visual Explanation:**The diagram has empty spaces with indicators suggesting that additional calculations or values are needed for $ t_{\text{critical}} $. It highlights the range where the critical $ t $-value will be placed, awaiting further input or calculation.This example illustrates how to determine the p-value range and how to use the t-distribution to validate your hypothesis testing results. **Statistical Analysis of Children Living with Grandparents**According to the U.S. Census Bureau, 11% of children in the United States lived with at least one grandparent in 2009 (*USA TODAY*, June 30, 2011). Suppose that in a recent sample of 1550 children, 226 were found to be living with at least one grandparent. At a 5% significance level, can you conclude that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%? Use both the *p*-value and the critical-value approaches.**Instructions:**Round your answers for the observed value of *z* and the critical value of *z* to two decimal places, and the *p*-value to four decimal places.- $ Z_{\text{observed}} = $ [Input Field]- $ p\text{-value} = $ [Input Field]- Critical value = [Input Field]**Graph/Diagram Explanation:**There are no graphs or diagrams in this text.

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Description: I added these two problems together because i thought since i only need help with one part of the random sample 17 i can myself another question help. I can't find the critical value for it. I tried -2.583 and 2.583 and my professor says it still wro

Answered: Arandom sample of 1/ observations taken…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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I added these two problems together because i thought since i only need help with one part of the random sample 17 i can myself another question help. I can't find the critical value for it. I tried -2.583 and 2.583 and my professor says it still wrong. If this problem can be specified on how to get it exactly with the correct answer it will be gladly appreciated

the other problem i need help with the 3 empty boxes.

please and thank you

### Hypothesis Testing Example

A random sample of 17 observations taken from a normally distributed population produced a sample mean of 42.4 and a standard deviation of 8. Find the range for the p-value and the critical and observed values of $ t $ for the following test of hypotheses, using $ \alpha = 0.01 $.

**Objective:**

Use the t-distribution table to find a range for the p-value. Round your answers for the values of $ t $ to three decimal places.

**Hypothesis:**

- $ H_0: \mu = 46 $
- $ H_1: \mu < 46 $

**p-value Range:**

- $ 0.025 < \text{p-value} < 0.05 $

**Critical Value and Observed Value:**

- $ t_{\text{critical}}: $ (Value to be determined using a t-distribution table)
- Observed $ t $ value: $ t_{\text{observed}} = -1.856 $

**Visual Explanation:**

The diagram has empty spaces with indicators suggesting that additional calculations or values are needed for $ t_{\text{critical}} $. It highlights the range where the critical $ t $-value will be placed, awaiting further input or calculation.

This example illustrates how to determine the p-value range and how to use the t-distribution to validate your hypothesis testing results.

**Statistical Analysis of Children Living with Grandparents**

According to the U.S. Census Bureau, 11% of children in the United States lived with at least one grandparent in 2009 (*USA TODAY*, June 30, 2011). Suppose that in a recent sample of 1550 children, 226 were found to be living with at least one grandparent. At a 5% significance level, can you conclude that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%? Use both the *p*-value and the critical-value approaches.

**Instructions:**

Round your answers for the observed value of *z* and the critical value of *z* to two decimal places, and the *p*-value to four decimal places.

- $ Z_{\text{observed}} = $ [Input Field]
- $ p\text{-value} = $ [Input Field]
- Critical value = [Input Field]

**Graph/Diagram Explanation:**
There are no graphs or diagrams in this text.

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As per the honor code, We’ll answer the first question since the exact one wasn’t specified. Please submit a new question by specifying the one you’d like answered in the remaining questions

Given,

$x = 42.4 s = 8 α = 0.01$

To find,

t critical value.

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